Counterfactuals in Science

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The term counterfactual is short for "counter-to-fact conditional," a statement about what would have been true, had certain facts been differentfor example, "Had the specimen been heated, it would have melted." On the face of it, claims about what would or could have happened appear speculative or even scientifically suspect because science is an investigation of reality grounded in experimental evidence, and by definition people have experimental access only to the actual universe. Yet, despite their implicit reference to alternative possibilities, many counterfactuals are scientifically respectable because the criteria determining whether they are true depend wholly on facts about the actual universe. Counterfactuals are often important in science because they appear implicitly in the definitions of certain specific concepts such as "solubility" and "biological fitness," and because they are close-ly related to general scientific notions such as "law of nature" and "causation."

The exact definition of counterfactual is controversial. In philosophy, a counterfactual is a statement that can be paraphrased in the form, "If A were true, then C would be true." They are distinguished from indicative conditionals, which take the form, "If A is true, then C is true." The difference in meaning consists roughly in the kind of facts one keeps fixed when considering the hypothetical situation A. To evaluate "If Napoleon Bonaparte had been born in Spain, France would have been ruled by democrats," one imagines Napoleon for some reason being born in Spain instead of Corsica and then speculates about alternative histories for France, ignoring what is known about the specifics of Napoleon's actual reign of power. But when evaluating the indicative, "If Napoleon was born in Spain, France was ruled by democrats," one can imagine that somehow historians have made a mistake on this one issue of Napoleon's birth and retain other things known about Napoleon, such as his undemocratic rule of France.

Despite the clear difference in meaning between these two particular sentences, there is significant controversy about whether the distinction between indicatives and counterfactuals makes sense in general and whether it is the best way to categorize conditionals. Associated with such debates are subtleties regarding how truth applies to counterfactuals. For example, the name "counterfactual" is misleading in that one can use counterfactuals for situations that are known to be true. Believing "If the fish had mutated, it would have survived," is consistent with believing the fish did mutate. So, counterfactuals are not only about counter-to-fact possibilities, but sometimes about actual situations as well.

Relation to Laws

What makes counterfactuals especially suitable for science is that the truth of counterfactuals depends largely on the general patterns that science aims to describe. One can reasonably say that a particular sample of salt is soluble in water even when the salt has never been dissolved and never will, on the grounds that because of its chemical structure, had it been placed in a sufficient amount of pure water, it would have dissolved. One is justified in making claims about what the salt counterfactually would have done in virtue of what other similar samples of salt have actually done and that person's knowledge of nature's regularities. In this way, the laws of nature can be understood as governing not only actual happenings but also what may have happened.

In one early philosophical treatment, Nelson Goodman tried to explain counterfactuals as a kind of elliptical expression. He thought counterfactuals such as, "Had I struck this match, it would have lit," should be understood as, "I struck this match and the laws of nature are true and logically entails that the match lit," where the ellipses represent some unstated but true facts. In a typical situation one may complete the sentence as, "I struck this match, and the laws of nature are true, and the match was dry, and there was sufficient oxygen in the air, and the match had the proper chemicals in the tip, entails that the match lit." The value of Goodman's account is that it captures the idea that counterfactuals in science express consequences of actual or hypothetical facts following from the laws of nature.

A major problem with this account, as Goodman himself recognized, is that it fails to give any constructive advice about how to pick out the right facts to insert into the ellipses. Why should one insert the fact that the match was dry and infer that the match would have lit, rather than insert that the match did not light and infer that the match would have been wet? Because there is no principled way of answering this question, Goodman's theory is of limited value as a guide to determining the truth of counterfactual statements. Also, because many counterfactuals have nothing to do with laws ("If the circumference were only half as large, the radius would be ") and some require the actual laws to be abandoned ("If there were no friction "), the elliptical account is not a general account of counterfactuals, and it was not immediately obvious how it would fit into a larger account.

Similarity Approaches

The dominant approach to elucidating the meaning of counterfactuals is to think of them as having truth conditions given by similarity relations among possible worldsthat is, hypothetical universesand more controversially that some more or less tractable notion of similarity tells how to evaluate specific counterfactuals. The justification for this is primarily formal. Robert Stalnaker and David Lewis developed a compelling family of logic systems describing counterfactual conditionals that do a remarkable job of justifying a wide range of intuitively plausible reasoning patterns. It is a feature of the logic that it can be interpreted using a notion of similarity among possible worlds. The way it works roughly is that the counterfactual "If A were the case, then C would be the case," is true when the worlds most similar to actuality among those where A is true are also worlds where C is true. Consider, "If this bird had three legs, it would have more legs than wings." The worlds where A is true are all the worlds where the bird has three legs, including worlds where it has three legs and three wings, worlds where it has three legs and four wings, and worlds where it has three legs, two wings, transparent feathers and a metallic beak. Intuitively, the minimal departure from actuality is for it to have one extra leg without any change to its wings, and so using common sense, one would say this counterfactual is true.

This illustration of how to determine whether a counterfactual is true involves an appeal to one's offhand, pretheoretical judgements of similarity, an appeal not mandated by the role similarity plays in the formal logic. It is a significant speculative leap to suppose that which counterfactuals are true depends on what human beings find similar. Nevertheless, inspired by David Lewis's work, there has been a serious philosophical research program dedicated to finding a plausible refinement of people's ordinary similarity concept to justify the usage of counterfactuals and more important to use counterfactuals in elucidating other concepts, such as causation.


A large part of science is figuring out what causes what. The role of counterfactuals in this project is to express dependencies among logically independent elements of reality, dependencies that are often causal. In the vast literature on causation, counterfactuals appear in different roles, not all of them central. One tradition concerning causation is to take causal connections between facts or events to be primitive elements of reality holding together the pattern of various particular facts. In this tradition, counterfactuals are not crucial to the formulation or definition of causation, although they are useful for expressing consequences of causal relations.

Where counterfactuals become most important are in theories where causes are understood as the byproduct of physical processes that are themselves not fundamentally causal in nature. This tradition is compelling because fundamental physics uses equations establishing mathematical relationships between physical entities in a way that does not obviously indicate what causes what. Here a theory about counterfactual relationships between events can be constructed as part of a story that tells how the mathematical relations in physics could possibly account for truths such as "Lightning causes thunder."

Some theories of causation are literally counterfactual accounts of causation. They argue that the causal connection is really due to a counterfactual dependence relation. An event E counterfactually depends on the event C whenever if C had not happened, E would not have happened. In one famous version of the theoryby David Lewiscausation is identified with having a chain of events that are counterfactually dependent on one another, but other variations on the connection between causation and counterfactual dependence are possible. While counterfactual accounts need to successfully explain many aspects of causation, for them to be even superficially plausible, they need to explain the causal asymmetrywhy in ordinary circumstances causes precede their effects. In counterfactual accounts, the difficult part of that explanation is to say why in an ordinary case of causation such as lightning causing thunder, one does not also have the lightning counterfactually depending on the thunder, wrongly entailing that thunder causes lightning.

Explaining why thunder does not cause lightning is difficult if one followsthe orthodoxy of using anthropocentric ideas of similarity as a guide to counterfactual truth. It is plausible that lightning counterfactually does depend on thunder because a possible world with a bolt of perfectly silent lightning is intuitively stranger than a world with just one less bolt of lightning. This shortcoming for the counterfactual account of causation may be corrected by giving up on using naive judgements of similarity and instead concocting a suitable theory of similarity that fits the needs of causation. David Lewis's theory in "Counterfactual Dependence and Time's Arrow" (1979) has been a popular model for developing such an account. In following this strategy, the attempt is to defend the more general hypothesis that counterfactuals ordinarily exhibit a temporal asymmetry that in turn explains the difference between cause and effect.

Counterfactual Asymmetry

When one considers how things may have been had only X not happened, typically one envisions alternate histories with an identical past where for some reason X did not happen. one then speculates how these alternate histories may have played out, leaving the future as open as the laws and circumstances allow. The practice of evaluating counterfactuals this way is asymmetric, treating the future but not the past as counterfactually dependent on the present.

Because there are counterfactuals having nothing to do with time, such as "If the variable x had been equal to three, then x +1 would have been equal to four," it is known that time asymmetry is not a part of the logic or meaning of counterfactuals per se. In a sense, it is wholly up to a person to choose whether he or she evaluate a given counterfactual symmetrically or asymmetrically. Nevertheless, it is an objective fact that nature tends to reward people for using the asymmetric ones. For example, it is sometimes useful to think, "If I were to shield myself now, I would avoid the next volley of arrows," and not so useful to think, "If I were to shield myself now, I would have avoided the previous volley." In this sense, counterfactual asymmetry is a natural fact perhaps amenable to scientific explanation. The project is to determine which physical structures vindicate the practice of evaluating counterfactuals asymmetrically. This includes determining to what extent the asymmetry is an aspect of people's particular perspective on nature, and to what extent the asymmetry is a feature of broader physical conditions and laws.

One idea is that there are fundamentally random processes that make the future chancy in a way that the past is not. This is problematic because although chances seem to imply a sense of openness for the future, it is not clear how chances imply a fixed past. Perhaps the intuition about chance in this case presupposes a theory where the past is given special fundamental significance as being in some sense more real than the future, or real in a different way. Spelling out such a deep metaphysical difference between past and future has proven difficult in itself, and clarification of its connection to chances has been problematic because the application of chances in science does not seem to require any such distinction.

Another group of proposed candidates for the explanation do not take counterfactual asymmetry to be a fundamental fact about reality or time itself, but as a contingent feature of the particular environment. A suggestion by Lewis is that typical processes exhibit a pattern where future facts "overdetermine" past facts in the sense that they give redundant evidence of the past. For example, after an explosion, there are many fragments around, each of which individually suggests an explosion, but there are often only a few facts beforehand that imply an explosion will occurfor example, a burning fuse.

Another idea is that counterfactual asymmetry is explained by cosmological facts, such as the universe is expanding from a smooth distribution of matter just after the big bang. This idea draws some plausibility from nature's two classes of time asymmetries. The first kind is a local asymmetrya fact that applies directly to the physical process taking place. Examples of this first kind include chancy transitions in the physical state, and time-asymmetric evolutions such as one sees in certain high energy particle experiments involving weak decays. The second kind is an asymmetry in the boundary conditions. Irreversible phenomena such as mixing gasses or a hot and cool object settling to a single temperature are explained only when one posits special boundary conditions. Specifically, the explanation for why people regularly see thermodynamic asymmetries comes by way of the physics of the distant past being constrained in a way that the future is not. The connection to counterfactuals is that one's reason for thinking that causation is asymmetric comes from one's experience with asymmetric macroscopic phenomena, exactly the kind of phenomena whose asymmetries are explained by boundary conditions and not by local asymmetries. Hence, it is plausible to think that special facts about the beginning of the universe are a critical component of why counterfactuals and causation treat the past as more fixedthat is, why nature rewards people for evaluating counterfactuals in a way that treats the past as fixed.

These strategies that attempt to explain counterfactual asymmetry by way of contingent physical circumstances are interesting in that they allow for at least some counterfactual dependence of the past on the future. This seems reasonable because one wants to allow for counterfactual differences that arise from ordinary processes. If the population were greater right now than it actually is, this would have been because people would have had more children, not because people would have magically popped into existence. While having some counterfactual dependence of the past on the present is good for matching up the theory of counterfactual evaluation with pretheoretical intuitions about counterfactuals, it highlights a difficulty with the desired uses of counterfactual asymmetry. If the past counterfactually depends on the present, and the difference between cause and effect is purely given by the counterfactual asymmetry, then one would seem to have backwards causation, such as thunder causing lightning. So either counterfactual asymmetry can't do the job of grounding the cause-effect asymmetry or causation is a less robust notion than is ordinarily thought, defined with respect to a temporal asymmetry that at best is justified only in certain special casesfor example, human decisionswhere there is little or no significant backwards dependence.

See also Causation: Philosophy of Science; Conditionals; Counterfactuals; Philosophy of Statistical Mechanics.


Goodman, Nelson. "The Problem of Counterfactual Conditionals." The Journal of Philosophy 44 (1947): 113128.

Lewis, David. "Causation," The Journal of Philosophy 70 (1973): 556567.

Lewis, David. "Counterfactual Dependence and Time's Arrow." Noûs 13 (1979): 455476.

Lewis, David. Counterfactuals. Oxford: Blackwell, 1973.

Stalnaker, Robert. "A Theory of Conditionals." In Studies in Logical Theory: American Philosophical Quarterly Monograph Series, no. 2, edited by Nicholas Rescher. Oxford: Basil Blackwell, 1968.

Douglas Kutach (2005)